Lesson HOW TO algebreze and solve these problems?
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<H2>HOW TO algebreze and solve these problems?<H2> <H3>Problem 1</H3>There were 50 more pupils who took the mathematics exam than took the geology exam. A fifth of those who took the mathematics exam were girls and a quarter of those who took the geology exam were girls. If the number of girls who took the mathematics exam was six more than the number of girls who took the geology exam, find the number of pupils who took the maths exam. <B>Solution</B> <pre> Let m = # of pupils who took the mathematics exam, and g = # of pupils who took the geology exam. We are given that m - g = 50, (1) it is our first equation. Now, "A fifth of those who took the mathematics exam were girls" - their number is {{{m/5}}}. (2) "A quarter of those who took the geology exam were girls" - their number is {{{g/4}}}. (3) We also are given that "the number of girls who took the mathematics exam was six more than the number of girls who took the geology exam". In other words, the number (2) is 6 more than the number (3), i.e. {{{m/5 - g/4}}} = 6. (4) Thus we have now the system of two equations in two unknowns (1) and (4). Let me rewrite them one more time: m - g = 50, (1) {{{m/5 - g/4}}} = 6. (4) Actually, the problem is just solved - the system of equations is established. The rest is just technique. To solve the system, multiply (1) by 4 and multiply (4) by 20 (both sides). You will get 4m - 4g = 200, (1') 4m - 5g = 120. (4') Next, distract (4') from (1'). You will get g = 200 - 120 = 80. Then from (1), m = 50 + g = 50 + 80 = 130. <U>Answer</U>. The number of pupils who took the maths exam is 130. </pre> <H3>Problem 2</H3>A school has 1025 students. A total of 400 students can not swim. This consists of 1/5 of the boys and 4/7 of the girls. If x boys can swim, write an equation for x and solve it. How many boys are there in the school? <B>Solution</B> <pre> It will be easier if we find out how many boys & girls are in the school. Let b = no. of boys in the school Let g = no. of girls : b + g = 1025 the number of girls & boys who can't swim are given as 400 {{{1/5}}}b + {{{4/7}}}g = 400 Get rid of the denominators, multiply by 35 7b + 20g = 14000 multiply the 1st equation by 7, subtract from the above equation 7b + 20g = 14000 7b + 7g = 7125 ------------------subtraction eliminates b, find g 0 + 13g = 6825 g = 6825/13 g = 525 girls in the school then 1025 - 525 = 500 boys in the school "If x boys can swim, write an equation for x and solve it." x = 500({{{5/5}}}- {{{1/5}}}) x = 500({{{4/5}}}) x = 400 boys can swim </pre> My other lessons on Miscellaneous word problems in this site are <TABLE> <TR> <TD> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/Some-Logic-problems.lesson>Some logic problems</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/HOW-TO-algebreze-and-to-solve-word-problems-on-numbers.lesson>How to algebreze and to solve word problems on numbers?</A> - <A HREF=http://www.algebra.com/algebra/homework/word/misc/Problem-on-two-wheels-and-three-wheels-bicycles-in-a-sale.lesson>Problem on two-wheel and three-wheel bicycles</A> - 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